LMFDB - Embedded newform 3525.2.a.bf.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,2,Mod(1,3525)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3525.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3525.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$28.1472667125$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 9x^{8} + 29x^{7} + 25x^{6} - 91x^{5} - 21x^{4} + 101x^{3} + 6x^{2} - 30x - 4 $ x^10 - 3x^9 - 9x^8 + 29x^7 + 25x^6 - 91x^5 - 21x^4 + 101x^3 + 6x^2 - 30*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 705)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.49126$ of defining polynomial
Character	$\chi$	$=$	3525.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.49126 q^{2} +1.00000 q^{3} +0.223857 q^{4} -1.49126 q^{6} +1.33606 q^{7} +2.64869 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.49126 q^{2} +1.00000 q^{3} +0.223857 q^{4} -1.49126 q^{6} +1.33606 q^{7} +2.64869 q^{8} +1.00000 q^{9} +3.95638 q^{11} +0.223857 q^{12} +0.0410899 q^{13} -1.99241 q^{14} -4.39760 q^{16} -6.69389 q^{17} -1.49126 q^{18} -5.69401 q^{19} +1.33606 q^{21} -5.90000 q^{22} +4.16638 q^{23} +2.64869 q^{24} -0.0612758 q^{26} +1.00000 q^{27} +0.299086 q^{28} -7.48398 q^{29} +0.727923 q^{31} +1.26059 q^{32} +3.95638 q^{33} +9.98233 q^{34} +0.223857 q^{36} -5.03176 q^{37} +8.49126 q^{38} +0.0410899 q^{39} -2.90659 q^{41} -1.99241 q^{42} -5.70025 q^{43} +0.885665 q^{44} -6.21316 q^{46} -1.00000 q^{47} -4.39760 q^{48} -5.21495 q^{49} -6.69389 q^{51} +0.00919828 q^{52} -5.79623 q^{53} -1.49126 q^{54} +3.53881 q^{56} -5.69401 q^{57} +11.1606 q^{58} -13.3302 q^{59} -4.38784 q^{61} -1.08552 q^{62} +1.33606 q^{63} +6.91534 q^{64} -5.90000 q^{66} +14.9200 q^{67} -1.49847 q^{68} +4.16638 q^{69} -15.2350 q^{71} +2.64869 q^{72} -12.9221 q^{73} +7.50366 q^{74} -1.27465 q^{76} +5.28596 q^{77} -0.0612758 q^{78} +15.3290 q^{79} +1.00000 q^{81} +4.33448 q^{82} +13.7297 q^{83} +0.299086 q^{84} +8.50056 q^{86} -7.48398 q^{87} +10.4792 q^{88} -4.68480 q^{89} +0.0548986 q^{91} +0.932675 q^{92} +0.727923 q^{93} +1.49126 q^{94} +1.26059 q^{96} +8.64892 q^{97} +7.77684 q^{98} +3.95638 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 3 * q^2 + 10 * q^3 + 7 * q^4 - 3 * q^6 - 9 * q^8 + 10 * q^9	$ 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9} - 16 q^{11} + 7 q^{12} - q^{13} - 12 q^{14} - 3 q^{16} - 14 q^{17} - 3 q^{18} - 26 q^{19} - 7 q^{23} - 9 q^{24} - 10 q^{26} + 10 q^{27} + 24 q^{28} - 14 q^{29} - 22 q^{31} - 11 q^{32} - 16 q^{33} - 12 q^{34} + 7 q^{36} - 2 q^{37} + 2 q^{38} - q^{39} - 22 q^{41} - 12 q^{42} + 11 q^{43} - 36 q^{44} - 14 q^{46} - 10 q^{47} - 3 q^{48} + 2 q^{49} - 14 q^{51} - 14 q^{52} - 22 q^{53} - 3 q^{54} - 48 q^{56} - 26 q^{57} + 20 q^{58} - 37 q^{59} - 25 q^{61} + 2 q^{62} - 7 q^{64} + 4 q^{67} - 8 q^{68} - 7 q^{69} - 27 q^{71} - 9 q^{72} - q^{73} + 4 q^{74} - 42 q^{76} - 34 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{81} + 32 q^{82} - 2 q^{83} + 24 q^{84} - 6 q^{86} - 14 q^{87} + 58 q^{88} + 9 q^{89} - 64 q^{91} - 34 q^{92} - 22 q^{93} + 3 q^{94} - 11 q^{96} + 40 q^{97} - 29 q^{98} - 16 q^{99}+O(q^{100}) $ 10 * q - 3 * q^2 + 10 * q^3 + 7 * q^4 - 3 * q^6 - 9 * q^8 + 10 * q^9 - 16 * q^11 + 7 * q^12 - q^13 - 12 * q^14 - 3 * q^16 - 14 * q^17 - 3 * q^18 - 26 * q^19 - 7 * q^23 - 9 * q^24 - 10 * q^26 + 10 * q^27 + 24 * q^28 - 14 * q^29 - 22 * q^31 - 11 * q^32 - 16 * q^33 - 12 * q^34 + 7 * q^36 - 2 * q^37 + 2 * q^38 - q^39 - 22 * q^41 - 12 * q^42 + 11 * q^43 - 36 * q^44 - 14 * q^46 - 10 * q^47 - 3 * q^48 + 2 * q^49 - 14 * q^51 - 14 * q^52 - 22 * q^53 - 3 * q^54 - 48 * q^56 - 26 * q^57 + 20 * q^58 - 37 * q^59 - 25 * q^61 + 2 * q^62 - 7 * q^64 + 4 * q^67 - 8 * q^68 - 7 * q^69 - 27 * q^71 - 9 * q^72 - q^73 + 4 * q^74 - 42 * q^76 - 34 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^81 + 32 * q^82 - 2 * q^83 + 24 * q^84 - 6 * q^86 - 14 * q^87 + 58 * q^88 + 9 * q^89 - 64 * q^91 - 34 * q^92 - 22 * q^93 + 3 * q^94 - 11 * q^96 + 40 * q^97 - 29 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.49126	−1.05448	−0.527240	−	0.849716i	$-0.676773\pi$
$2$	−1.49126	−1.05448	−0.527240	+	0.849716i	$0.676773\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.223857	0.111929
$5$	0	0
$5$	0	0
$6$	−1.49126	−0.608804
$7$	1.33606	0.504983	0.252491	−	0.967599i	$-0.418750\pi$
$7$	1.33606	0.504983	0.252491	+	0.967599i	$0.418750\pi$
$8$	2.64869	0.936454
$9$	1.00000	0.333333
$10$	0	0
$11$	3.95638	1.19289	0.596447	−	0.802652i	$-0.296578\pi$
$11$	3.95638	1.19289	0.596447	+	0.802652i	$0.296578\pi$
$12$	0.223857	0.0646220
$13$	0.0410899	0.0113963	0.00569815	−	0.999984i	$-0.498186\pi$
$13$	0.0410899	0.0113963	0.00569815	+	0.999984i	$0.498186\pi$
$14$	−1.99241	−0.532494
$15$	0	0
$16$	−4.39760	−1.09940
$17$	−6.69389	−1.62351	−0.811753	−	0.584001i	$-0.801486\pi$
$17$	−6.69389	−1.62351	−0.811753	+	0.584001i	$0.801486\pi$
$18$	−1.49126	−0.351493
$19$	−5.69401	−1.30630	−0.653148	−	0.757230i	$-0.726552\pi$
$19$	−5.69401	−1.30630	−0.653148	+	0.757230i	$0.726552\pi$
$20$	0	0
$21$	1.33606	0.291552
$22$	−5.90000	−1.25788
$23$	4.16638	0.868751	0.434375	−	0.900732i	$-0.356969\pi$
$23$	4.16638	0.868751	0.434375	+	0.900732i	$0.356969\pi$
$24$	2.64869	0.540662
$25$	0	0
$26$	−0.0612758	−0.0120172
$27$	1.00000	0.192450
$28$	0.299086	0.0565220
$29$	−7.48398	−1.38974	−0.694870	−	0.719136i	$-0.744538\pi$
$29$	−7.48398	−1.38974	−0.694870	+	0.719136i	$0.744538\pi$
$30$	0	0
$31$	0.727923	0.130739	0.0653694	−	0.997861i	$-0.479177\pi$
$31$	0.727923	0.130739	0.0653694	+	0.997861i	$0.479177\pi$
$32$	1.26059	0.222843
$33$	3.95638	0.688718
$34$	9.98233	1.71195
$35$	0	0
$36$	0.223857	0.0373095
$37$	−5.03176	−0.827216	−0.413608	−	0.910455i	$-0.635732\pi$
$37$	−5.03176	−0.827216	−0.413608	+	0.910455i	$0.635732\pi$
$38$	8.49126	1.37746
$39$	0.0410899	0.00657966
$40$	0	0
$41$	−2.90659	−0.453932	−0.226966	−	0.973903i	$-0.572881\pi$
$41$	−2.90659	−0.453932	−0.226966	+	0.973903i	$0.572881\pi$
$42$	−1.99241	−0.307436
$43$	−5.70025	−0.869280	−0.434640	−	0.900604i	$-0.643124\pi$
$43$	−5.70025	−0.869280	−0.434640	+	0.900604i	$0.643124\pi$
$44$	0.885665	0.133519
$45$	0	0
$46$	−6.21316	−0.916081
$47$	−1.00000	−0.145865
$47$	−1.00000	−0.145865
$48$	−4.39760	−0.634739
$49$	−5.21495	−0.744993
$50$	0	0
$51$	−6.69389	−0.937331
$52$	0.00919828	0.00127557
$53$	−5.79623	−0.796174	−0.398087	−	0.917348i	$-0.630326\pi$
$53$	−5.79623	−0.796174	−0.398087	+	0.917348i	$0.630326\pi$
$54$	−1.49126	−0.202935
$55$	0	0
$56$	3.53881	0.472893
$57$	−5.69401	−0.754190
$58$	11.1606	1.46545
$59$	−13.3302	−1.73544	−0.867719	−	0.497055i	$-0.834415\pi$
$59$	−13.3302	−1.73544	−0.867719	+	0.497055i	$0.834415\pi$
$60$	0	0
$61$	−4.38784	−0.561805	−0.280902	−	0.959736i	$-0.590634\pi$
$61$	−4.38784	−0.561805	−0.280902	+	0.959736i	$0.590634\pi$
$62$	−1.08552	−0.137861
$63$	1.33606	0.168328
$64$	6.91534	0.864418
$65$	0	0
$66$	−5.90000	−0.726240
$67$	14.9200	1.82277	0.911383	−	0.411560i	$-0.135016\pi$
$67$	14.9200	1.82277	0.911383	+	0.411560i	$0.135016\pi$
$68$	−1.49847	−0.181717
$69$	4.16638	0.501574
$70$	0	0
$71$	−15.2350	−1.80806	−0.904031	−	0.427466i	$-0.859406\pi$
$71$	−15.2350	−1.80806	−0.904031	+	0.427466i	$0.859406\pi$
$72$	2.64869	0.312151
$73$	−12.9221	−1.51242	−0.756210	−	0.654329i	$-0.772951\pi$
$73$	−12.9221	−1.51242	−0.756210	+	0.654329i	$0.772951\pi$
$74$	7.50366	0.872283
$75$	0	0
$76$	−1.27465	−0.146212
$77$	5.28596	0.602391
$78$	−0.0612758	−0.00693812
$79$	15.3290	1.72464	0.862322	−	0.506360i	$-0.169009\pi$
$79$	15.3290	1.72464	0.862322	+	0.506360i	$0.169009\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	4.33448	0.478663
$83$	13.7297	1.50703	0.753514	−	0.657431i	$-0.228357\pi$
$83$	13.7297	1.50703	0.753514	+	0.657431i	$0.228357\pi$
$84$	0.299086	0.0326330
$85$	0	0
$86$	8.50056	0.916639
$87$	−7.48398	−0.802366
$88$	10.4792	1.11709
$89$	−4.68480	−0.496588	−0.248294	−	0.968685i	$-0.579870\pi$
$89$	−4.68480	−0.496588	−0.248294	+	0.968685i	$0.579870\pi$
$90$	0	0
$91$	0.0548986	0.00575493
$92$	0.932675	0.0972381
$93$	0.727923	0.0754821
$94$	1.49126	0.153812
$95$	0	0
$96$	1.26059	0.128658
$97$	8.64892	0.878164	0.439082	−	0.898447i	$-0.355304\pi$
$97$	8.64892	0.878164	0.439082	+	0.898447i	$0.355304\pi$
$98$	7.77684	0.785580
$99$	3.95638	0.397632
$100$	0	0
$101$	−11.0905	−1.10355	−0.551774	−	0.833994i	$-0.686049\pi$
$101$	−11.0905	−1.10355	−0.551774	+	0.833994i	$0.686049\pi$
$102$	9.98233	0.988398
$103$	7.30204	0.719492	0.359746	−	0.933050i	$-0.382863\pi$
$103$	7.30204	0.719492	0.359746	+	0.933050i	$0.382863\pi$
$104$	0.108835	0.0106721
$105$	0	0
$106$	8.64369	0.839549
$107$	1.65045	0.159555	0.0797776	−	0.996813i	$-0.474579\pi$
$107$	1.65045	0.159555	0.0797776	+	0.996813i	$0.474579\pi$
$108$	0.223857	0.0215407
$109$	−0.956668	−0.0916321	−0.0458161	−	0.998950i	$-0.514589\pi$
$109$	−0.956668	−0.0916321	−0.0458161	+	0.998950i	$0.514589\pi$
$110$	0	0
$111$	−5.03176	−0.477593
$112$	−5.87545	−0.555178
$113$	9.62581	0.905520	0.452760	−	0.891632i	$-0.350439\pi$
$113$	9.62581	0.905520	0.452760	+	0.891632i	$0.350439\pi$
$114$	8.49126	0.795279
$115$	0	0
$116$	−1.67534	−0.155552
$117$	0.0410899	0.00379877
$118$	19.8787	1.82999
$119$	−8.94342	−0.819842
$120$	0	0
$121$	4.65298	0.422998
$122$	6.54341	0.592412
$123$	−2.90659	−0.262078
$124$	0.162951	0.0146334
$125$	0	0
$126$	−1.99241	−0.177498
$127$	9.80920	0.870426	0.435213	−	0.900328i	$-0.356673\pi$
$127$	9.80920	0.870426	0.435213	+	0.900328i	$0.356673\pi$
$128$	−12.8337	−1.13435
$129$	−5.70025	−0.501879
$130$	0	0
$131$	6.95672	0.607812	0.303906	−	0.952702i	$-0.401709\pi$
$131$	6.95672	0.607812	0.303906	+	0.952702i	$0.401709\pi$
$132$	0.885665	0.0770873
$133$	−7.60753	−0.659657
$134$	−22.2496	−1.92207
$135$	0	0
$136$	−17.7300	−1.52034
$137$	1.76638	0.150912	0.0754560	−	0.997149i	$-0.475959\pi$
$137$	1.76638	0.150912	0.0754560	+	0.997149i	$0.475959\pi$
$138$	−6.21316	−0.528899
$139$	−14.5812	−1.23676	−0.618380	−	0.785879i	$-0.712211\pi$
$139$	−14.5812	−1.23676	−0.618380	+	0.785879i	$0.712211\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	22.7194	1.90657
$143$	0.162568	0.0135946
$144$	−4.39760	−0.366467
$145$	0	0
$146$	19.2702	1.59482
$147$	−5.21495	−0.430122
$148$	−1.12640	−0.0925891
$149$	−10.2641	−0.840865	−0.420433	−	0.907324i	$-0.638122\pi$
$149$	−10.2641	−0.840865	−0.420433	+	0.907324i	$0.638122\pi$
$150$	0	0
$151$	−6.37876	−0.519096	−0.259548	−	0.965730i	$-0.583574\pi$
$151$	−6.37876	−0.519096	−0.259548	+	0.965730i	$0.583574\pi$
$152$	−15.0817	−1.22329
$153$	−6.69389	−0.541169
$154$	−7.88274	−0.635209
$155$	0	0
$156$	0.00919828	0.000736452 0
$157$	11.3052	0.902250	0.451125	−	0.892461i	$-0.351023\pi$
$157$	11.3052	0.902250	0.451125	+	0.892461i	$0.351023\pi$
$158$	−22.8595	−1.81860
$159$	−5.79623	−0.459671
$160$	0	0
$161$	5.56653	0.438704
$162$	−1.49126	−0.117164
$163$	10.5829	0.828918	0.414459	−	0.910068i	$-0.363971\pi$
$163$	10.5829	0.828918	0.414459	+	0.910068i	$0.363971\pi$
$164$	−0.650660	−0.0508080
$165$	0	0
$166$	−20.4745	−1.58913
$167$	−8.53831	−0.660714	−0.330357	−	0.943856i	$-0.607169\pi$
$167$	−8.53831	−0.660714	−0.330357	+	0.943856i	$0.607169\pi$
$168$	3.53881	0.273025
$169$	−12.9983	−0.999870
$170$	0	0
$171$	−5.69401	−0.435432
$172$	−1.27604	−0.0972974
$173$	−20.2593	−1.54028	−0.770141	−	0.637873i	$-0.779814\pi$
$173$	−20.2593	−1.54028	−0.770141	+	0.637873i	$0.779814\pi$
$174$	11.1606	0.846080
$175$	0	0
$176$	−17.3986	−1.31147
$177$	−13.3302	−1.00196
$178$	6.98625	0.523642
$179$	20.1939	1.50937	0.754683	−	0.656090i	$-0.227791\pi$
$179$	20.1939	1.50937	0.754683	+	0.656090i	$0.227791\pi$
$180$	0	0
$181$	−7.00047	−0.520341	−0.260170	−	0.965563i	$-0.583779\pi$
$181$	−7.00047	−0.520341	−0.260170	+	0.965563i	$0.583779\pi$
$182$	−0.0818680	−0.00606846
$183$	−4.38784	−0.324358
$184$	11.0355	0.813545
$185$	0	0
$186$	−1.08552	−0.0795943
$187$	−26.4836	−1.93667
$188$	−0.223857	−0.0163265
$189$	1.33606	0.0971839
$190$	0	0
$191$	−17.9866	−1.30146	−0.650731	−	0.759309i	$-0.725537\pi$
$191$	−17.9866	−1.30146	−0.650731	+	0.759309i	$0.725537\pi$
$192$	6.91534	0.499072
$193$	5.45134	0.392396	0.196198	−	0.980564i	$-0.437140\pi$
$193$	5.45134	0.392396	0.196198	+	0.980564i	$0.437140\pi$
$194$	−12.8978	−0.926007
$195$	0	0
$196$	−1.16740	−0.0833860
$197$	10.7734	0.767576	0.383788	−	0.923421i	$-0.374619\pi$
$197$	10.7734	0.767576	0.383788	+	0.923421i	$0.374619\pi$
$198$	−5.90000	−0.419295
$199$	9.32085	0.660737	0.330369	−	0.943852i	$-0.392827\pi$
$199$	9.32085	0.660737	0.330369	+	0.943852i	$0.392827\pi$
$200$	0	0
$201$	14.9200	1.05237
$202$	16.5389	1.16367
$203$	−9.99903	−0.701794
$204$	−1.49847	−0.104914
$205$	0	0
$206$	−10.8892	−0.758690
$207$	4.16638	0.289584
$208$	−0.180697	−0.0125291
$209$	−22.5277	−1.55827
$210$	0	0
$211$	2.63574	0.181452	0.0907258	−	0.995876i	$-0.471081\pi$
$211$	2.63574	0.181452	0.0907258	+	0.995876i	$0.471081\pi$
$212$	−1.29753	−0.0891146
$213$	−15.2350	−1.04389
$214$	−2.46125	−0.168248
$215$	0	0
$216$	2.64869	0.180221
$217$	0.972547	0.0660208
$218$	1.42664	0.0966243
$219$	−12.9221	−0.873196
$220$	0	0
$221$	−0.275051	−0.0185020
$222$	7.50366	0.503613
$223$	10.6703	0.714536	0.357268	−	0.934002i	$-0.383708\pi$
$223$	10.6703	0.714536	0.357268	+	0.934002i	$0.383708\pi$
$224$	1.68422	0.112532
$225$	0	0
$226$	−14.3546	−0.954853
$227$	14.4678	0.960265	0.480132	−	0.877196i	$-0.340589\pi$
$227$	14.4678	0.960265	0.480132	+	0.877196i	$0.340589\pi$
$228$	−1.27465	−0.0844155
$229$	2.42710	0.160387	0.0801935	−	0.996779i	$-0.474446\pi$
$229$	2.42710	0.160387	0.0801935	+	0.996779i	$0.474446\pi$
$230$	0	0
$231$	5.28596	0.347791
$232$	−19.8227	−1.30143
$233$	−26.8074	−1.75621	−0.878105	−	0.478468i	$-0.841192\pi$
$233$	−26.8074	−1.75621	−0.878105	+	0.478468i	$0.841192\pi$
$234$	−0.0612758	−0.00400572
$235$	0	0
$236$	−2.98405	−0.194245
$237$	15.3290	0.995724
$238$	13.3370	0.864507
$239$	9.26735	0.599455	0.299728	−	0.954025i	$-0.403104\pi$
$239$	9.26735	0.599455	0.299728	+	0.954025i	$0.403104\pi$
$240$	0	0
$241$	13.0989	0.843772	0.421886	−	0.906649i	$-0.361368\pi$
$241$	13.0989	0.843772	0.421886	+	0.906649i	$0.361368\pi$
$242$	−6.93880	−0.446043
$243$	1.00000	0.0641500
$244$	−0.982249	−0.0628821
$245$	0	0
$246$	4.33448	0.276356
$247$	−0.233967	−0.0148869
$248$	1.92804	0.122431
$249$	13.7297	0.870083
$250$	0	0
$251$	−19.7237	−1.24495	−0.622475	−	0.782640i	$-0.713873\pi$
$251$	−19.7237	−1.24495	−0.622475	+	0.782640i	$0.713873\pi$
$252$	0.299086	0.0188407
$253$	16.4838	1.03633
$254$	−14.6281	−0.917847
$255$	0	0
$256$	5.30778	0.331736
$257$	−24.1225	−1.50472	−0.752360	−	0.658752i	$-0.771085\pi$
$257$	−24.1225	−1.50472	−0.752360	+	0.658752i	$0.771085\pi$
$258$	8.50056	0.529222
$259$	−6.72272	−0.417730
$260$	0	0
$261$	−7.48398	−0.463247
$262$	−10.3743	−0.640926
$263$	−23.2111	−1.43126	−0.715630	−	0.698480i	$-0.753860\pi$
$263$	−23.2111	−1.43126	−0.715630	+	0.698480i	$0.753860\pi$
$264$	10.4792	0.644953
$265$	0	0
$266$	11.3448	0.695595
$267$	−4.68480	−0.286705
$268$	3.33995	0.204020
$269$	−2.70597	−0.164986	−0.0824928	−	0.996592i	$-0.526288\pi$
$269$	−2.70597	−0.164986	−0.0824928	+	0.996592i	$0.526288\pi$
$270$	0	0
$271$	26.3044	1.59788	0.798938	−	0.601413i	$-0.205395\pi$
$271$	26.3044	1.59788	0.798938	+	0.601413i	$0.205395\pi$
$272$	29.4370	1.78488
$273$	0.0548986	0.00332261
$274$	−2.63413	−0.159134
$275$	0	0
$276$	0.932675	0.0561404
$277$	−16.1779	−0.972035	−0.486017	−	0.873949i	$-0.661551\pi$
$277$	−16.1779	−0.972035	−0.486017	+	0.873949i	$0.661551\pi$
$278$	21.7443	1.30414
$279$	0.727923	0.0435796
$280$	0	0
$281$	−15.5980	−0.930499	−0.465250	−	0.885180i	$-0.654035\pi$
$281$	−15.5980	−0.930499	−0.465250	+	0.885180i	$0.654035\pi$
$282$	1.49126	0.0888033
$283$	−5.10329	−0.303359	−0.151680	−	0.988430i	$-0.548468\pi$
$283$	−5.10329	−0.303359	−0.151680	+	0.988430i	$0.548468\pi$
$284$	−3.41047	−0.202374
$285$	0	0
$286$	−0.242431	−0.0143352
$287$	−3.88337	−0.229228
$288$	1.26059	0.0742808
$289$	27.8081	1.63577
$290$	0	0
$291$	8.64892	0.507008
$292$	−2.89271	−0.169283
$293$	−33.6381	−1.96516	−0.982578	−	0.185849i	$-0.940496\pi$
$293$	−33.6381	−1.96516	−0.982578	+	0.185849i	$0.940496\pi$
$294$	7.77684	0.453555
$295$	0	0
$296$	−13.3276	−0.774649
$297$	3.95638	0.229573
$298$	15.3064	0.886676
$299$	0.171196	0.00990054
$300$	0	0
$301$	−7.61587	−0.438971
$302$	9.51239	0.547377
$303$	−11.0905	−0.637134
$304$	25.0400	1.43614
$305$	0	0
$306$	9.98233	0.570652
$307$	−29.1813	−1.66546	−0.832731	−	0.553677i	$-0.813224\pi$
$307$	−29.1813	−1.66546	−0.832731	+	0.553677i	$0.813224\pi$
$308$	1.18330	0.0674248
$309$	7.30204	0.415399
$310$	0	0
$311$	15.0237	0.851914	0.425957	−	0.904743i	$-0.359937\pi$
$311$	15.0237	0.851914	0.425957	+	0.904743i	$0.359937\pi$
$312$	0.108835	0.00616154
$313$	5.65747	0.319779	0.159890	−	0.987135i	$-0.448886\pi$
$313$	5.65747	0.319779	0.159890	+	0.987135i	$0.448886\pi$
$314$	−16.8589	−0.951404
$315$	0	0
$316$	3.43150	0.193037
$317$	−7.18475	−0.403536	−0.201768	−	0.979433i	$-0.564669\pi$
$317$	−7.18475	−0.403536	−0.201768	+	0.979433i	$0.564669\pi$
$318$	8.64369	0.484714
$319$	−29.6095	−1.65781
$320$	0	0
$321$	1.65045	0.0921192
$322$	−8.30115	−0.462605
$323$	38.1151	2.12078
$324$	0.223857	0.0124365
$325$	0	0
$326$	−15.7819	−0.874077
$327$	−0.956668	−0.0529038
$328$	−7.69865	−0.425087
$329$	−1.33606	−0.0736593
$330$	0	0
$331$	−6.33141	−0.348006	−0.174003	−	0.984745i	$-0.555670\pi$
$331$	−6.33141	−0.348006	−0.174003	+	0.984745i	$0.555670\pi$
$332$	3.07349	0.168680
$333$	−5.03176	−0.275739
$334$	12.7328	0.696710
$335$	0	0
$336$	−5.87545	−0.320532
$337$	−10.7733	−0.586859	−0.293429	−	0.955981i	$-0.594797\pi$
$337$	−10.7733	−0.586859	−0.293429	+	0.955981i	$0.594797\pi$
$338$	19.3839	1.05434
$339$	9.62581	0.522802
$340$	0	0
$341$	2.87994	0.155958
$342$	8.49126	0.459155
$343$	−16.3199	−0.881191
$344$	−15.0982	−0.814041
$345$	0	0
$346$	30.2118	1.62420
$347$	5.31635	0.285397	0.142698	−	0.989766i	$-0.454422\pi$
$347$	5.31635	0.285397	0.142698	+	0.989766i	$0.454422\pi$
$348$	−1.67534	−0.0898078
$349$	13.4716	0.721118	0.360559	−	0.932736i	$-0.382586\pi$
$349$	13.4716	0.721118	0.360559	+	0.932736i	$0.382586\pi$
$350$	0	0
$351$	0.0410899	0.00219322
$352$	4.98737	0.265828
$353$	11.5955	0.617167	0.308584	−	0.951197i	$-0.400145\pi$
$353$	11.5955	0.617167	0.308584	+	0.951197i	$0.400145\pi$
$354$	19.8787	1.05654
$355$	0	0
$356$	−1.04873	−0.0555824
$357$	−8.94342	−0.473336
$358$	−30.1144	−1.59160
$359$	31.8068	1.67870	0.839349	−	0.543594i	$-0.182937\pi$
$359$	31.8068	1.67870	0.839349	+	0.543594i	$0.182937\pi$
$360$	0	0
$361$	13.4218	0.706410
$362$	10.4395	0.548689
$363$	4.65298	0.244218
$364$	0.0122894	0.000644142 0
$365$	0	0
$366$	6.54341	0.342029
$367$	29.5268	1.54129	0.770643	−	0.637267i	$-0.219935\pi$
$367$	29.5268	1.54129	0.770643	+	0.637267i	$0.219935\pi$
$368$	−18.3221	−0.955105
$369$	−2.90659	−0.151311
$370$	0	0
$371$	−7.74410	−0.402054
$372$	0.162951	0.00844860
$373$	−15.7126	−0.813567	−0.406784	−	0.913525i	$-0.633350\pi$
$373$	−15.7126	−0.813567	−0.406784	+	0.913525i	$0.633350\pi$
$374$	39.4939	2.04218
$375$	0	0
$376$	−2.64869	−0.136596
$377$	−0.307516	−0.0158379
$378$	−1.99241	−0.102479
$379$	11.7012	0.601048	0.300524	−	0.953774i	$-0.402838\pi$
$379$	11.7012	0.601048	0.300524	+	0.953774i	$0.402838\pi$
$380$	0	0
$381$	9.80920	0.502541
$382$	26.8226	1.37237
$383$	10.9122	0.557587	0.278794	−	0.960351i	$-0.410065\pi$
$383$	10.9122	0.557587	0.278794	+	0.960351i	$0.410065\pi$
$384$	−12.8337	−0.654919
$385$	0	0
$386$	−8.12937	−0.413774
$387$	−5.70025	−0.289760
$388$	1.93612	0.0982917
$389$	0.756182	0.0383399	0.0191700	−	0.999816i	$-0.493898\pi$
$389$	0.756182	0.0383399	0.0191700	+	0.999816i	$0.493898\pi$
$390$	0	0
$391$	−27.8893	−1.41042
$392$	−13.8128	−0.697651
$393$	6.95672	0.350920
$394$	−16.0660	−0.809394
$395$	0	0
$396$	0.885665	0.0445064
$397$	13.3378	0.669406	0.334703	−	0.942324i	$-0.391364\pi$
$397$	13.3378	0.669406	0.334703	+	0.942324i	$0.391364\pi$
$398$	−13.8998	−0.696735
$399$	−7.60753	−0.380853
$400$	0	0
$401$	21.2304	1.06020	0.530098	−	0.847936i	$-0.322155\pi$
$401$	21.2304	1.06020	0.530098	+	0.847936i	$0.322155\pi$
$402$	−22.2496	−1.10971
$403$	0.0299103	0.00148994
$404$	−2.48269	−0.123519
$405$	0	0
$406$	14.9112	0.740028
$407$	−19.9076	−0.986782
$408$	−17.7300	−0.877768
$409$	−1.86339	−0.0921385	−0.0460693	−	0.998938i	$-0.514669\pi$
$409$	−1.86339	−0.0921385	−0.0460693	+	0.998938i	$0.514669\pi$
$410$	0	0
$411$	1.76638	0.0871291
$412$	1.63462	0.0805317
$413$	−17.8099	−0.876366
$414$	−6.21316	−0.305360
$415$	0	0
$416$	0.0517975	0.00253958
$417$	−14.5812	−0.714044
$418$	33.5947	1.64317
$419$	2.40878	0.117677	0.0588383	−	0.998268i	$-0.481260\pi$
$419$	2.40878	0.117677	0.0588383	+	0.998268i	$0.481260\pi$
$420$	0	0
$421$	−23.2256	−1.13195	−0.565974	−	0.824423i	$-0.691500\pi$
$421$	−23.2256	−1.13195	−0.565974	+	0.824423i	$0.691500\pi$
$422$	−3.93057	−0.191337
$423$	−1.00000	−0.0486217
$424$	−15.3524	−0.745580
$425$	0	0
$426$	22.7194	1.10076
$427$	−5.86241	−0.283702
$428$	0.369466	0.0178588
$429$	0.162568	0.00784884
$430$	0	0
$431$	−15.8418	−0.763075	−0.381537	−	0.924353i	$-0.624605\pi$
$431$	−15.8418	−0.763075	−0.381537	+	0.924353i	$0.624605\pi$
$432$	−4.39760	−0.211580
$433$	−17.2105	−0.827086	−0.413543	−	0.910485i	$-0.635709\pi$
$433$	−17.2105	−0.827086	−0.413543	+	0.910485i	$0.635709\pi$
$434$	−1.45032	−0.0696176
$435$	0	0
$436$	−0.214157	−0.0102563
$437$	−23.7234	−1.13485
$438$	19.2702	0.920768
$439$	−28.1289	−1.34252	−0.671259	−	0.741223i	$-0.734246\pi$
$439$	−28.1289	−1.34252	−0.671259	+	0.741223i	$0.734246\pi$
$440$	0	0
$441$	−5.21495	−0.248331
$442$	0.410173	0.0195099
$443$	−2.41901	−0.114930	−0.0574652	−	0.998348i	$-0.518302\pi$
$443$	−2.41901	−0.114930	−0.0574652	+	0.998348i	$0.518302\pi$
$444$	−1.12640	−0.0534564
$445$	0	0
$446$	−15.9122	−0.753464
$447$	−10.2641	−0.485474
$448$	9.23930	0.436516
$449$	−17.6406	−0.832512	−0.416256	−	0.909248i	$-0.636658\pi$
$449$	−17.6406	−0.832512	−0.416256	+	0.909248i	$0.636658\pi$
$450$	0	0
$451$	−11.4996	−0.541494
$452$	2.15481	0.101354
$453$	−6.37876	−0.299700
$454$	−21.5753	−1.01258
$455$	0	0
$456$	−15.0817	−0.706264
$457$	37.6972	1.76340	0.881699	−	0.471812i	$-0.156400\pi$
$457$	37.6972	1.76340	0.881699	+	0.471812i	$0.156400\pi$
$458$	−3.61943	−0.169125
$459$	−6.69389	−0.312444
$460$	0	0
$461$	−29.9929	−1.39691	−0.698454	−	0.715655i	$-0.746128\pi$
$461$	−29.9929	−1.39691	−0.698454	+	0.715655i	$0.746128\pi$
$462$	−7.88274	−0.366738
$463$	8.99642	0.418099	0.209050	−	0.977905i	$-0.432963\pi$
$463$	8.99642	0.418099	0.209050	+	0.977905i	$0.432963\pi$
$464$	32.9116	1.52788
$465$	0	0
$466$	39.9768	1.85189
$467$	12.1293	0.561279	0.280640	−	0.959813i	$-0.409453\pi$
$467$	12.1293	0.561279	0.280640	+	0.959813i	$0.409453\pi$
$468$	0.00919828	0.000425191 0
$469$	19.9340	0.920465
$470$	0	0
$471$	11.3052	0.520914
$472$	−35.3075	−1.62516
$473$	−22.5524	−1.03696
$474$	−22.8595	−1.04997
$475$	0	0
$476$	−2.00205	−0.0917638
$477$	−5.79623	−0.265391
$478$	−13.8200	−0.632114
$479$	−2.08391	−0.0952161	−0.0476081	−	0.998866i	$-0.515160\pi$
$479$	−2.08391	−0.0952161	−0.0476081	+	0.998866i	$0.515160\pi$
$480$	0	0
$481$	−0.206755	−0.00942720
$482$	−19.5338	−0.889740
$483$	5.56653	0.253286
$484$	1.04160	0.0473456
$485$	0	0
$486$	−1.49126	−0.0676449
$487$	6.70756	0.303949	0.151974	−	0.988384i	$-0.451437\pi$
$487$	6.70756	0.303949	0.151974	+	0.988384i	$0.451437\pi$
$488$	−11.6220	−0.526104
$489$	10.5829	0.478576
$490$	0	0
$491$	−31.4777	−1.42057	−0.710285	−	0.703914i	$-0.751434\pi$
$491$	−31.4777	−1.42057	−0.710285	+	0.703914i	$0.751434\pi$
$492$	−0.650660	−0.0293340
$493$	50.0969	2.25625
$494$	0.348905	0.0156980
$495$	0	0
$496$	−3.20111	−0.143734
$497$	−20.3549	−0.913040
$498$	−20.4745	−0.917486
$499$	−20.0811	−0.898955	−0.449478	−	0.893292i	$-0.648390\pi$
$499$	−20.0811	−0.898955	−0.449478	+	0.893292i	$0.648390\pi$
$500$	0	0
$501$	−8.53831	−0.381464
$502$	29.4132	1.31277
$503$	14.6931	0.655135	0.327567	−	0.944828i	$-0.393771\pi$
$503$	14.6931	0.655135	0.327567	+	0.944828i	$0.393771\pi$
$504$	3.53881	0.157631
$505$	0	0
$506$	−24.5817	−1.09279
$507$	−12.9983	−0.577275
$508$	2.19586	0.0974256
$509$	−27.1134	−1.20178	−0.600890	−	0.799332i	$-0.705187\pi$
$509$	−27.1134	−1.20178	−0.600890	+	0.799332i	$0.705187\pi$
$510$	0	0
$511$	−17.2647	−0.763746
$512$	17.7522	0.784545
$513$	−5.69401	−0.251397
$514$	35.9729	1.58670
$515$	0	0
$516$	−1.27604	−0.0561747
$517$	−3.95638	−0.174002
$518$	10.0253	0.440488
$519$	−20.2593	−0.889282
$520$	0	0
$521$	9.80741	0.429670	0.214835	−	0.976650i	$-0.431079\pi$
$521$	9.80741	0.429670	0.214835	+	0.976650i	$0.431079\pi$
$522$	11.1606	0.488484
$523$	9.32826	0.407896	0.203948	−	0.978982i	$-0.434623\pi$
$523$	9.32826	0.407896	0.203948	+	0.978982i	$0.434623\pi$
$524$	1.55731	0.0680315
$525$	0	0
$526$	34.6138	1.50923
$527$	−4.87263	−0.212255
$528$	−17.3986	−0.757177
$529$	−5.64125	−0.245272
$530$	0	0
$531$	−13.3302	−0.578479
$532$	−1.70300	−0.0738345
$533$	−0.119431	−0.00517315
$534$	6.98625	0.302325
$535$	0	0
$536$	39.5184	1.70694
$537$	20.1939	0.871432
$538$	4.03530	0.173974
$539$	−20.6323	−0.888698
$540$	0	0
$541$	−0.416268	−0.0178967	−0.00894837	−	0.999960i	$-0.502848\pi$
$541$	−0.416268	−0.0178967	−0.00894837	+	0.999960i	$0.502848\pi$
$542$	−39.2267	−1.68493
$543$	−7.00047	−0.300419
$544$	−8.43823	−0.361786
$545$	0	0
$546$	−0.0818680	−0.00350363
$547$	0.189446	0.00810013	0.00405007	−	0.999992i	$-0.498711\pi$
$547$	0.189446	0.00810013	0.00405007	+	0.999992i	$0.498711\pi$
$548$	0.395417	0.0168914
$549$	−4.38784	−0.187268
$550$	0	0
$551$	42.6139	1.81541
$552$	11.0355	0.469700
$553$	20.4804	0.870915
$554$	24.1254	1.02499
$555$	0	0
$556$	−3.26410	−0.138429
$557$	−25.8465	−1.09515	−0.547576	−	0.836756i	$-0.684449\pi$
$557$	−25.8465	−1.09515	−0.547576	+	0.836756i	$0.684449\pi$
$558$	−1.08552	−0.0459538
$559$	−0.234223	−0.00990658
$560$	0	0
$561$	−26.4836	−1.11814
$562$	23.2607	0.981193
$563$	24.1557	1.01804	0.509021	−	0.860754i	$-0.330007\pi$
$563$	24.1557	1.01804	0.509021	+	0.860754i	$0.330007\pi$
$564$	−0.223857	−0.00942609
$565$	0	0
$566$	7.61033	0.319886
$567$	1.33606	0.0561092
$568$	−40.3528	−1.69317
$569$	24.1361	1.01184	0.505919	−	0.862581i	$-0.331153\pi$
$569$	24.1361	1.01184	0.505919	+	0.862581i	$0.331153\pi$
$570$	0	0
$571$	5.80442	0.242907	0.121454	−	0.992597i	$-0.461244\pi$
$571$	5.80442	0.242907	0.121454	+	0.992597i	$0.461244\pi$
$572$	0.0363919	0.00152162
$573$	−17.9866	−0.751399
$574$	5.79111	0.241716
$575$	0	0
$576$	6.91534	0.288139
$577$	22.8280	0.950344	0.475172	−	0.879893i	$-0.342386\pi$
$577$	22.8280	0.950344	0.475172	+	0.879893i	$0.342386\pi$
$578$	−41.4691	−1.72489
$579$	5.45134	0.226550
$580$	0	0
$581$	18.3437	0.761023
$582$	−12.8978	−0.534630
$583$	−22.9321	−0.949751
$584$	−34.2267	−1.41631
$585$	0	0
$586$	50.1631	2.07222
$587$	28.4503	1.17427	0.587135	−	0.809489i	$-0.300256\pi$
$587$	28.4503	1.17427	0.587135	+	0.809489i	$0.300256\pi$
$588$	−1.16740	−0.0481429
$589$	−4.14480	−0.170784
$590$	0	0
$591$	10.7734	0.443160
$592$	22.1277	0.909442
$593$	−8.26303	−0.339322	−0.169661	−	0.985503i	$-0.554267\pi$
$593$	−8.26303	−0.339322	−0.169661	+	0.985503i	$0.554267\pi$
$594$	−5.90000	−0.242080
$595$	0	0
$596$	−2.29769	−0.0941169
$597$	9.32085	0.381477
$598$	−0.255298	−0.0104399
$599$	−0.574161	−0.0234596	−0.0117298	−	0.999931i	$-0.503734\pi$
$599$	−0.574161	−0.0234596	−0.0117298	+	0.999931i	$0.503734\pi$
$600$	0	0
$601$	17.0446	0.695262	0.347631	−	0.937631i	$-0.386986\pi$
$601$	17.0446	0.695262	0.347631	+	0.937631i	$0.386986\pi$
$602$	11.3572	0.462887
$603$	14.9200	0.607588
$604$	−1.42793	−0.0581017
$605$	0	0
$606$	16.5389	0.671845
$607$	−22.8467	−0.927321	−0.463660	−	0.886013i	$-0.653464\pi$
$607$	−22.8467	−0.927321	−0.463660	+	0.886013i	$0.653464\pi$
$608$	−7.17780	−0.291098
$609$	−9.99903	−0.405181
$610$	0	0
$611$	−0.0410899	−0.00166232
$612$	−1.49847	−0.0605723
$613$	15.5322	0.627338	0.313669	−	0.949532i	$-0.398442\pi$
$613$	15.5322	0.627338	0.313669	+	0.949532i	$0.398442\pi$
$614$	43.5169	1.75620
$615$	0	0
$616$	14.0009	0.564111
$617$	29.3687	1.18234	0.591169	−	0.806548i	$-0.298667\pi$
$617$	29.3687	1.18234	0.591169	+	0.806548i	$0.298667\pi$
$618$	−10.8892	−0.438030
$619$	−17.7422	−0.713117	−0.356559	−	0.934273i	$-0.616050\pi$
$619$	−17.7422	−0.713117	−0.356559	+	0.934273i	$0.616050\pi$
$620$	0	0
$621$	4.16638	0.167191
$622$	−22.4042	−0.898326
$623$	−6.25916	−0.250768
$624$	−0.180697	−0.00723368
$625$	0	0
$626$	−8.43677	−0.337201
$627$	−22.5277	−0.899670
$628$	2.53074	0.100988
$629$	33.6820	1.34299
$630$	0	0
$631$	24.7735	0.986219	0.493109	−	0.869967i	$-0.335860\pi$
$631$	24.7735	0.986219	0.493109	+	0.869967i	$0.335860\pi$
$632$	40.6017	1.61505
$633$	2.63574	0.104761
$634$	10.7143	0.425520
$635$	0	0
$636$	−1.29753	−0.0514503
$637$	−0.214282	−0.00849016
$638$	44.1554	1.74813
$639$	−15.2350	−0.602687
$640$	0	0
$641$	36.8836	1.45682	0.728408	−	0.685144i	$-0.240261\pi$
$641$	36.8836	1.45682	0.728408	+	0.685144i	$0.240261\pi$
$642$	−2.46125	−0.0971379
$643$	−12.9077	−0.509030	−0.254515	−	0.967069i	$-0.581916\pi$
$643$	−12.9077	−0.509030	−0.254515	+	0.967069i	$0.581916\pi$
$644$	1.24611	0.0491035
$645$	0	0
$646$	−56.8395	−2.23632
$647$	−11.0990	−0.436348	−0.218174	−	0.975910i	$-0.570010\pi$
$647$	−11.0990	−0.436348	−0.218174	+	0.975910i	$0.570010\pi$
$648$	2.64869	0.104050
$649$	−52.7392	−2.07019
$650$	0	0
$651$	0.972547	0.0381171
$652$	2.36906	0.0927796
$653$	−39.9476	−1.56327	−0.781635	−	0.623736i	$-0.785614\pi$
$653$	−39.9476	−1.56327	−0.781635	+	0.623736i	$0.785614\pi$
$654$	1.42664	0.0557861
$655$	0	0
$656$	12.7820	0.499054
$657$	−12.9221	−0.504140
$658$	1.99241	0.0776723
$659$	27.1718	1.05846	0.529231	−	0.848478i	$-0.322480\pi$
$659$	27.1718	1.05846	0.529231	+	0.848478i	$0.322480\pi$
$660$	0	0
$661$	25.9254	1.00838	0.504191	−	0.863592i	$-0.331791\pi$
$661$	25.9254	1.00838	0.504191	+	0.863592i	$0.331791\pi$
$662$	9.44178	0.366965
$663$	−0.275051	−0.0106821
$664$	36.3657	1.41126
$665$	0	0
$666$	7.50366	0.290761
$667$	−31.1811	−1.20734
$668$	−1.91136	−0.0739529
$669$	10.6703	0.412538
$670$	0	0
$671$	−17.3600	−0.670174
$672$	1.68422	0.0649701
$673$	7.12018	0.274463	0.137231	−	0.990539i	$-0.456180\pi$
$673$	7.12018	0.274463	0.137231	+	0.990539i	$0.456180\pi$
$674$	16.0658	0.618831
$675$	0	0
$676$	−2.90977	−0.111914
$677$	−16.1591	−0.621046	−0.310523	−	0.950566i	$-0.600504\pi$
$677$	−16.1591	−0.621046	−0.310523	+	0.950566i	$0.600504\pi$
$678$	−14.3546	−0.551285
$679$	11.5555	0.443458
$680$	0	0
$681$	14.4678	0.554409
$682$	−4.29474	−0.164454
$683$	22.3426	0.854915	0.427457	−	0.904036i	$-0.359409\pi$
$683$	22.3426	0.854915	0.427457	+	0.904036i	$0.359409\pi$
$684$	−1.27465	−0.0487373
$685$	0	0
$686$	24.3372	0.929198
$687$	2.42710	0.0925995
$688$	25.0674	0.955687
$689$	−0.238167	−0.00907343
$690$	0	0
$691$	−19.3114	−0.734642	−0.367321	−	0.930094i	$-0.619725\pi$
$691$	−19.3114	−0.734642	−0.367321	+	0.930094i	$0.619725\pi$
$692$	−4.53518	−0.172402
$693$	5.28596	0.200797
$694$	−7.92806	−0.300945
$695$	0	0
$696$	−19.8227	−0.751379
$697$	19.4563	0.736962
$698$	−20.0897	−0.760405
$699$	−26.8074	−1.01395
$700$	0	0
$701$	48.3676	1.82682	0.913409	−	0.407042i	$-0.133440\pi$
$701$	48.3676	1.82682	0.913409	+	0.407042i	$0.133440\pi$
$702$	−0.0612758	−0.00231271
$703$	28.6509	1.08059
$704$	27.3597	1.03116
$705$	0	0
$706$	−17.2919	−0.650791
$707$	−14.8176	−0.557273
$708$	−2.98405	−0.112148
$709$	4.64215	0.174340	0.0871698	−	0.996193i	$-0.472218\pi$
$709$	4.64215	0.174340	0.0871698	+	0.996193i	$0.472218\pi$
$710$	0	0
$711$	15.3290	0.574881
$712$	−12.4086	−0.465031
$713$	3.03280	0.113579
$714$	13.3370	0.499124
$715$	0	0
$716$	4.52056	0.168941
$717$	9.26735	0.346096
$718$	−47.4322	−1.77015
$719$	5.80041	0.216319	0.108159	−	0.994134i	$-0.465504\pi$
$719$	5.80041	0.216319	0.108159	+	0.994134i	$0.465504\pi$
$720$	0	0
$721$	9.75595	0.363331
$722$	−20.0154	−0.744895
$723$	13.0989	0.487152
$724$	−1.56711	−0.0582410
$725$	0	0
$726$	−6.93880	−0.257523
$727$	−41.5541	−1.54116	−0.770579	−	0.637345i	$-0.780033\pi$
$727$	−41.5541	−1.54116	−0.770579	+	0.637345i	$0.780033\pi$
$728$	0.145409	0.00538923
$729$	1.00000	0.0370370
$730$	0	0
$731$	38.1568	1.41128
$732$	−0.982249	−0.0363050
$733$	34.6874	1.28121	0.640605	−	0.767871i	$-0.278684\pi$
$733$	34.6874	1.28121	0.640605	+	0.767871i	$0.278684\pi$
$734$	−44.0322	−1.62526
$735$	0	0
$736$	5.25209	0.193595
$737$	59.0292	2.17437
$738$	4.33448	0.159554
$739$	17.3473	0.638130	0.319065	−	0.947733i	$-0.396631\pi$
$739$	17.3473	0.638130	0.319065	+	0.947733i	$0.396631\pi$
$740$	0	0
$741$	−0.233967	−0.00859498
$742$	11.5485	0.423958
$743$	−15.6303	−0.573421	−0.286710	−	0.958017i	$-0.592562\pi$
$743$	−15.6303	−0.573421	−0.286710	+	0.958017i	$0.592562\pi$
$744$	1.92804	0.0706854
$745$	0	0
$746$	23.4316	0.857891
$747$	13.7297	0.502343
$748$	−5.92854	−0.216769
$749$	2.20510	0.0805726
$750$	0	0
$751$	−14.6908	−0.536075	−0.268038	−	0.963408i	$-0.586375\pi$
$751$	−14.6908	−0.536075	−0.268038	+	0.963408i	$0.586375\pi$
$752$	4.39760	0.160364
$753$	−19.7237	−0.718772
$754$	0.458587	0.0167007
$755$	0	0
$756$	0.299086	0.0108777
$757$	−16.5774	−0.602515	−0.301258	−	0.953543i	$-0.597406\pi$
$757$	−16.5774	−0.602515	−0.301258	+	0.953543i	$0.597406\pi$
$758$	−17.4495	−0.633794
$759$	16.4838	0.598324
$760$	0	0
$761$	−35.7483	−1.29587	−0.647937	−	0.761694i	$-0.724368\pi$
$761$	−35.7483	−1.29587	−0.647937	+	0.761694i	$0.724368\pi$
$762$	−14.6281	−0.529919
$763$	−1.27816	−0.0462726
$764$	−4.02642	−0.145671
$765$	0	0
$766$	−16.2729	−0.587965
$767$	−0.547735	−0.0197776
$768$	5.30778	0.191528
$769$	−46.2771	−1.66879	−0.834397	−	0.551164i	$-0.814184\pi$
$769$	−46.2771	−1.66879	−0.834397	+	0.551164i	$0.814184\pi$
$770$	0	0
$771$	−24.1225	−0.868751
$772$	1.22032	0.0439204
$773$	−40.3104	−1.44986	−0.724932	−	0.688820i	$-0.758129\pi$
$773$	−40.3104	−1.44986	−0.724932	+	0.688820i	$0.758129\pi$
$774$	8.50056	0.305546
$775$	0	0
$776$	22.9083	0.822360
$777$	−6.72272	−0.241176
$778$	−1.12766	−0.0404287
$779$	16.5501	0.592970
$780$	0	0
$781$	−60.2755	−2.15683
$782$	41.5902	1.48726
$783$	−7.48398	−0.267455
$784$	22.9333	0.819045
$785$	0	0
$786$	−10.3743	−0.370039
$787$	33.1243	1.18076	0.590378	−	0.807127i	$-0.298979\pi$
$787$	33.1243	1.18076	0.590378	+	0.807127i	$0.298979\pi$
$788$	2.41171	0.0859137
$789$	−23.2111	−0.826338
$790$	0	0
$791$	12.8606	0.457272
$792$	10.4792	0.372364
$793$	−0.180296	−0.00640250
$794$	−19.8902	−0.705876
$795$	0	0
$796$	2.08654	0.0739554
$797$	−22.7431	−0.805601	−0.402800	−	0.915288i	$-0.631963\pi$
$797$	−22.7431	−0.805601	−0.402800	+	0.915288i	$0.631963\pi$
$798$	11.3448	0.401602
$799$	6.69389	0.236813
$800$	0	0
$801$	−4.68480	−0.165529
$802$	−31.6601	−1.11796
$803$	−51.1249	−1.80416
$804$	3.33995	0.117791
$805$	0	0
$806$	−0.0446040	−0.00157111
$807$	−2.70597	−0.0952545
$808$	−29.3754	−1.03342
$809$	−10.6421	−0.374156	−0.187078	−	0.982345i	$-0.559902\pi$
$809$	−10.6421	−0.374156	−0.187078	+	0.982345i	$0.559902\pi$
$810$	0	0
$811$	20.4955	0.719696	0.359848	−	0.933011i	$-0.382829\pi$
$811$	20.4955	0.719696	0.359848	+	0.933011i	$0.382829\pi$
$812$	−2.23836	−0.0785509
$813$	26.3044	0.922535
$814$	29.6874	1.04054
$815$	0	0
$816$	29.4370	1.03050
$817$	32.4573	1.13554
$818$	2.77879	0.0971582
$819$	0.0548986	0.00191831
$820$	0	0
$821$	29.9290	1.04453	0.522265	−	0.852783i	$-0.325087\pi$
$821$	29.9290	1.04453	0.522265	+	0.852783i	$0.325087\pi$
$822$	−2.63413	−0.0918759
$823$	4.74742	0.165485	0.0827423	−	0.996571i	$-0.473632\pi$
$823$	4.74742	0.165485	0.0827423	+	0.996571i	$0.473632\pi$
$824$	19.3409	0.673771
$825$	0	0
$826$	26.5591	0.924111
$827$	−26.6718	−0.927469	−0.463735	−	0.885974i	$-0.653491\pi$
$827$	−26.6718	−0.927469	−0.463735	+	0.885974i	$0.653491\pi$
$828$	0.932675	0.0324127
$829$	17.3861	0.603845	0.301922	−	0.953333i	$-0.402372\pi$
$829$	17.3861	0.603845	0.301922	+	0.953333i	$0.402372\pi$
$830$	0	0
$831$	−16.1779	−0.561204
$832$	0.284151	0.00985116
$833$	34.9083	1.20950
$834$	21.7443	0.752945
$835$	0	0
$836$	−5.04299	−0.174415
$837$	0.727923	0.0251607
$838$	−3.59212	−0.124088
$839$	25.9446	0.895707	0.447854	−	0.894107i	$-0.352189\pi$
$839$	25.9446	0.895707	0.447854	+	0.894107i	$0.352189\pi$
$840$	0	0
$841$	27.0099	0.931376
$842$	34.6354	1.19362
$843$	−15.5980	−0.537224
$844$	0.590029	0.0203096
$845$	0	0
$846$	1.49126	0.0512706
$847$	6.21665	0.213607
$848$	25.4895	0.875314
$849$	−5.10329	−0.175144
$850$	0	0
$851$	−20.9642	−0.718645
$852$	−3.41047	−0.116841
$853$	38.1799	1.30725	0.653627	−	0.756817i	$-0.273247\pi$
$853$	38.1799	1.30725	0.653627	+	0.756817i	$0.273247\pi$
$854$	8.74237	0.299158
$855$	0	0
$856$	4.37154	0.149416
$857$	−40.2741	−1.37574	−0.687869	−	0.725835i	$-0.741454\pi$
$857$	−40.2741	−1.37574	−0.687869	+	0.725835i	$0.741454\pi$
$858$	−0.242431	−0.00827644
$859$	−42.0209	−1.43373	−0.716867	−	0.697210i	$-0.754424\pi$
$859$	−42.0209	−1.43373	−0.716867	+	0.697210i	$0.754424\pi$
$860$	0	0
$861$	−3.88337	−0.132345
$862$	23.6243	0.804647
$863$	49.1260	1.67227	0.836134	−	0.548525i	$-0.184810\pi$
$863$	49.1260	1.67227	0.836134	+	0.548525i	$0.184810\pi$
$864$	1.26059	0.0428861
$865$	0	0
$866$	25.6654	0.872146
$867$	27.8081	0.944413
$868$	0.217712	0.00738962
$869$	60.6473	2.05732
$870$	0	0
$871$	0.613061	0.0207728
$872$	−2.53392	−0.0858093
$873$	8.64892	0.292721
$874$	35.3778	1.19667
$875$	0	0
$876$	−2.89271	−0.0977356
$877$	12.7166	0.429408	0.214704	−	0.976679i	$-0.431121\pi$
$877$	12.7166	0.429408	0.214704	+	0.976679i	$0.431121\pi$
$878$	41.9475	1.41566
$879$	−33.6381	−1.13458
$880$	0	0
$881$	−43.3268	−1.45972	−0.729859	−	0.683598i	$-0.760414\pi$
$881$	−43.3268	−1.45972	−0.729859	+	0.683598i	$0.760414\pi$
$882$	7.77684	0.261860
$883$	−1.27229	−0.0428160	−0.0214080	−	0.999771i	$-0.506815\pi$
$883$	−1.27229	−0.0428160	−0.0214080	+	0.999771i	$0.506815\pi$
$884$	−0.0615722	−0.00207090
$885$	0	0
$886$	3.60737	0.121192
$887$	8.80233	0.295553	0.147777	−	0.989021i	$-0.452788\pi$
$887$	8.80233	0.295553	0.147777	+	0.989021i	$0.452788\pi$
$888$	−13.3276	−0.447244
$889$	13.1057	0.439550
$890$	0	0
$891$	3.95638	0.132544
$892$	2.38862	0.0799770
$893$	5.69401	0.190543
$894$	15.3064	0.511922
$895$	0	0
$896$	−17.1466	−0.572829
$897$	0.171196	0.00571608
$898$	26.3067	0.877867
$899$	−5.44776	−0.181693
$900$	0	0
$901$	38.7993	1.29259
$902$	17.1488	0.570994
$903$	−7.61587	−0.253440
$904$	25.4958	0.847978
$905$	0	0
$906$	9.51239	0.316028
$907$	−17.5566	−0.582957	−0.291479	−	0.956577i	$-0.594147\pi$
$907$	−17.5566	−0.582957	−0.291479	+	0.956577i	$0.594147\pi$
$908$	3.23873	0.107481
$909$	−11.0905	−0.367849
$910$	0	0
$911$	36.0055	1.19292	0.596458	−	0.802645i	$-0.296574\pi$
$911$	36.0055	1.19292	0.596458	+	0.802645i	$0.296574\pi$
$912$	25.0400	0.829157
$913$	54.3199	1.79773
$914$	−56.2163	−1.85947
$915$	0	0
$916$	0.543323	0.0179519
$917$	9.29459	0.306934
$918$	9.98233	0.329466
$919$	39.3778	1.29895	0.649477	−	0.760381i	$-0.274988\pi$
$919$	39.3778	1.29895	0.649477	+	0.760381i	$0.274988\pi$
$920$	0	0
$921$	−29.1813	−0.961555
$922$	44.7272	1.47301
$923$	−0.626005	−0.0206052
$924$	1.18330	0.0389277
$925$	0	0
$926$	−13.4160	−0.440877
$927$	7.30204	0.239831
$928$	−9.43421	−0.309693
$929$	−58.8640	−1.93126	−0.965632	−	0.259913i	$-0.916306\pi$
$929$	−58.8640	−1.93126	−0.965632	+	0.259913i	$0.916306\pi$
$930$	0	0
$931$	29.6940	0.973181
$932$	−6.00103	−0.196570
$933$	15.0237	0.491853
$934$	−18.0880	−0.591858
$935$	0	0
$936$	0.108835	0.00355737
$937$	12.2677	0.400767	0.200384	−	0.979718i	$-0.435781\pi$
$937$	12.2677	0.400767	0.200384	+	0.979718i	$0.435781\pi$
$938$	−29.7267	−0.970612
$939$	5.65747	0.184625
$940$	0	0
$941$	51.9936	1.69494	0.847471	−	0.530842i	$-0.178124\pi$
$941$	51.9936	1.69494	0.847471	+	0.530842i	$0.178124\pi$
$942$	−16.8589	−0.549294
$943$	−12.1099	−0.394354
$944$	58.6207	1.90794
$945$	0	0
$946$	33.6315	1.09345
$947$	−52.0168	−1.69032	−0.845159	−	0.534514i	$-0.820495\pi$
$947$	−52.0168	−1.69032	−0.845159	+	0.534514i	$0.820495\pi$
$948$	3.43150	0.111450
$949$	−0.530969	−0.0172360
$950$	0	0
$951$	−7.18475	−0.232981
$952$	−23.6884	−0.767744
$953$	−1.76284	−0.0571041	−0.0285520	−	0.999592i	$-0.509090\pi$
$953$	−1.76284	−0.0571041	−0.0285520	+	0.999592i	$0.509090\pi$
$954$	8.64369	0.279850
$955$	0	0
$956$	2.07456	0.0670962
$957$	−29.6095	−0.957139
$958$	3.10765	0.100404
$959$	2.35999	0.0762079
$960$	0	0
$961$	−30.4701	−0.982907
$962$	0.308325	0.00994080
$963$	1.65045	0.0531851
$964$	2.93227	0.0944422
$965$	0	0
$966$	−8.30115	−0.267085
$967$	−23.6228	−0.759657	−0.379828	−	0.925057i	$-0.624017\pi$
$967$	−23.6228	−0.759657	−0.379828	+	0.925057i	$0.624017\pi$
$968$	12.3243	0.396118
$969$	38.1151	1.22443
$970$	0	0
$971$	11.1293	0.357156	0.178578	−	0.983926i	$-0.442850\pi$
$971$	11.1293	0.357156	0.178578	+	0.983926i	$0.442850\pi$
$972$	0.223857	0.00718022
$973$	−19.4813	−0.624542
$974$	−10.0027	−0.320508
$975$	0	0
$976$	19.2960	0.617649
$977$	−31.9269	−1.02143	−0.510717	−	0.859749i	$-0.670620\pi$
$977$	−31.9269	−1.02143	−0.510717	+	0.859749i	$0.670620\pi$
$978$	−15.7819	−0.504649
$979$	−18.5349	−0.592377
$980$	0	0
$981$	−0.956668	−0.0305440
$982$	46.9415	1.49796
$983$	−0.0136206	−0.000434430 0	−0.000217215	−	1.00000i	$-0.500069\pi$
$983$	−0.0136206	−0.000434430 0	−0.000217215		1.00000i	$0.500069\pi$
$984$	−7.69865	−0.245424
$985$	0	0
$986$	−74.7075	−2.37917
$987$	−1.33606	−0.0425272
$988$	−0.0523751	−0.00166628
$989$	−23.7494	−0.755188
$990$	0	0
$991$	14.6375	0.464975	0.232487	−	0.972599i	$-0.425314\pi$
$991$	14.6375	0.464975	0.232487	+	0.972599i	$0.425314\pi$
$992$	0.917610	0.0291342
$993$	−6.33141	−0.200921
$994$	30.3544	0.962783
$995$	0	0
$996$	3.07349	0.0973873
$997$	10.9289	0.346122	0.173061	−	0.984911i	$-0.444634\pi$
$997$	10.9289	0.346122	0.173061	+	0.984911i	$0.444634\pi$
$998$	29.9462	0.947931
$999$	−5.03176	−0.159198

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.2.a.bf.1.4		10
5.2	odd	4		705.2.c.b.424.6	✓	20
5.3	odd	4		705.2.c.b.424.15	yes	20
5.4	even	2		3525.2.a.bg.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.2.c.b.424.6	✓	20	5.2	odd	4
705.2.c.b.424.15	yes	20	5.3	odd	4
3525.2.a.bf.1.4		10	1.1	even	1	trivial
3525.2.a.bg.1.7		10	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3525.a (trivial)

\(f(q)\)	\(=\)	\(q-1.49126 q^{2} +1.00000 q^{3} +0.223857 q^{4} -1.49126 q^{6} +1.33606 q^{7} +2.64869 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.49126 q^{2} +1.00000 q^{3} +0.223857 q^{4} -1.49126 q^{6} +1.33606 q^{7} +2.64869 q^{8} +1.00000 q^{9} +3.95638 q^{11} +0.223857 q^{12} +0.0410899 q^{13} -1.99241 q^{14} -4.39760 q^{16} -6.69389 q^{17} -1.49126 q^{18} -5.69401 q^{19} +1.33606 q^{21} -5.90000 q^{22} +4.16638 q^{23} +2.64869 q^{24} -0.0612758 q^{26} +1.00000 q^{27} +0.299086 q^{28} -7.48398 q^{29} +0.727923 q^{31} +1.26059 q^{32} +3.95638 q^{33} +9.98233 q^{34} +0.223857 q^{36} -5.03176 q^{37} +8.49126 q^{38} +0.0410899 q^{39} -2.90659 q^{41} -1.99241 q^{42} -5.70025 q^{43} +0.885665 q^{44} -6.21316 q^{46} -1.00000 q^{47} -4.39760 q^{48} -5.21495 q^{49} -6.69389 q^{51} +0.00919828 q^{52} -5.79623 q^{53} -1.49126 q^{54} +3.53881 q^{56} -5.69401 q^{57} +11.1606 q^{58} -13.3302 q^{59} -4.38784 q^{61} -1.08552 q^{62} +1.33606 q^{63} +6.91534 q^{64} -5.90000 q^{66} +14.9200 q^{67} -1.49847 q^{68} +4.16638 q^{69} -15.2350 q^{71} +2.64869 q^{72} -12.9221 q^{73} +7.50366 q^{74} -1.27465 q^{76} +5.28596 q^{77} -0.0612758 q^{78} +15.3290 q^{79} +1.00000 q^{81} +4.33448 q^{82} +13.7297 q^{83} +0.299086 q^{84} +8.50056 q^{86} -7.48398 q^{87} +10.4792 q^{88} -4.68480 q^{89} +0.0548986 q^{91} +0.932675 q^{92} +0.727923 q^{93} +1.49126 q^{94} +1.26059 q^{96} +8.64892 q^{97} +7.77684 q^{98} +3.95638 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 3 * q^2 + 10 * q^3 + 7 * q^4 - 3 * q^6 - 9 * q^8 + 10 * q^9	\( 10 q - 3 q^{2} + 10 q^{3} + 7 q^{4} - 3 q^{6} - 9 q^{8} + 10 q^{9} - 16 q^{11} + 7 q^{12} - q^{13} - 12 q^{14} - 3 q^{16} - 14 q^{17} - 3 q^{18} - 26 q^{19} - 7 q^{23} - 9 q^{24} - 10 q^{26} + 10 q^{27} + 24 q^{28} - 14 q^{29} - 22 q^{31} - 11 q^{32} - 16 q^{33} - 12 q^{34} + 7 q^{36} - 2 q^{37} + 2 q^{38} - q^{39} - 22 q^{41} - 12 q^{42} + 11 q^{43} - 36 q^{44} - 14 q^{46} - 10 q^{47} - 3 q^{48} + 2 q^{49} - 14 q^{51} - 14 q^{52} - 22 q^{53} - 3 q^{54} - 48 q^{56} - 26 q^{57} + 20 q^{58} - 37 q^{59} - 25 q^{61} + 2 q^{62} - 7 q^{64} + 4 q^{67} - 8 q^{68} - 7 q^{69} - 27 q^{71} - 9 q^{72} - q^{73} + 4 q^{74} - 42 q^{76} - 34 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{81} + 32 q^{82} - 2 q^{83} + 24 q^{84} - 6 q^{86} - 14 q^{87} + 58 q^{88} + 9 q^{89} - 64 q^{91} - 34 q^{92} - 22 q^{93} + 3 q^{94} - 11 q^{96} + 40 q^{97} - 29 q^{98} - 16 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 + 10 * q^3 + 7 * q^4 - 3 * q^6 - 9 * q^8 + 10 * q^9 - 16 * q^11 + 7 * q^12 - q^13 - 12 * q^14 - 3 * q^16 - 14 * q^17 - 3 * q^18 - 26 * q^19 - 7 * q^23 - 9 * q^24 - 10 * q^26 + 10 * q^27 + 24 * q^28 - 14 * q^29 - 22 * q^31 - 11 * q^32 - 16 * q^33 - 12 * q^34 + 7 * q^36 - 2 * q^37 + 2 * q^38 - q^39 - 22 * q^41 - 12 * q^42 + 11 * q^43 - 36 * q^44 - 14 * q^46 - 10 * q^47 - 3 * q^48 + 2 * q^49 - 14 * q^51 - 14 * q^52 - 22 * q^53 - 3 * q^54 - 48 * q^56 - 26 * q^57 + 20 * q^58 - 37 * q^59 - 25 * q^61 + 2 * q^62 - 7 * q^64 + 4 * q^67 - 8 * q^68 - 7 * q^69 - 27 * q^71 - 9 * q^72 - q^73 + 4 * q^74 - 42 * q^76 - 34 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^81 + 32 * q^82 - 2 * q^83 + 24 * q^84 - 6 * q^86 - 14 * q^87 + 58 * q^88 + 9 * q^89 - 64 * q^91 - 34 * q^92 - 22 * q^93 + 3 * q^94 - 11 * q^96 + 40 * q^97 - 29 * q^98 - 16 * q^99

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